Can I claim miles driving clients around during the day?

I work in home health and take my client out on a daily basis. I drive him to lunch, we go shopping, we go out in the community. This is part of his care plan and it is a requirement of my job. Can I claim these miles? If so, how do I log them? From point-to-point, for example: I drive my client to lunch, then we go to the community center, then back home. Do I log each "leg" separately like this:

Client's house to Restaurant (lunch) 8 miles.

Restaurant to Community center 5 miles.

community center to client's home 13 miles.

If not, how do I go about logging this hypothetical day?


Thank you very much in advance!